Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015 EE 1106 : Introduction to EE Freshman...

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

EE 1106: Introduction to EEFreshman Practicum

Lecture-Lab: Introduction to signals and systems, RLC dynamical circuit

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Signals and Systems

– Signal: • Any time dependent physical quantity• Constant – DC, Variable - AC• Electrical, Optical, Mechanical

– System:• Object in which input signals interact to

produce output signals.• Linear System has some have fundamental

properties that make it predictable: – Sinusoid in, sinusoid out of same frequency

(when transients settle)– Double the amplitude in, double the amplitude

out (when initial state conditions are zero)?

x(t)

u(t) y(t)

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

System Modeling

• Building mathematical models based on observed data, or other insight for the system.– Parametric models (analytical): ODE, PDE– Non-parametric models: graphical models -

plots, look-up cause-effect tables– Mental models – Driving a car and using the

cause-effect knowledge– Simulation models – Many interconnect

subroutines, objects in video game

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Types of Models

• White Box – derived from first principles laws: physical,

chemical, biological, economical, etc.– Examples: RLC circuits, MSD mechanical

models (electromechanical system models).

• Black Box – model is entirely derived from measured data– Example: regression (data fit)

• Gray Box – combination of the two

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

White Box Systems: Electrical

• Defined by Electro-Magnetic Laws of Physics: Ohm’s Law, Kirchoff’s Laws, Maxwell’s Equations

• Example: Resistor, Capacitor, Inductor

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Physics of an Inductor

Truncated hollow cylinder of permeability, area, A, andlength lm.

Coil ofN turns

Flux linkage,

Core flux,

Coil current, i

i+-

A

lmN

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Voltage Drop Across Inductor

Note Passive SignConvention

Li

+ v -+ -

2 2

m m

d d N Ai N A div

dt dt l l dt

2

m

N AL

l

di

v Ldt

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Energy in an Inductor

Stored Energy

Li

+ v -+ -

dip vi Li

dt pdt dw Li di

21

2W Lidi Li

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Physics of a Capacitor

Plate separationdistance, g

Plate area, ACurrent, i, and

Charge, q.

Dielectric material ofpermittivity, .

Voltageacross

platesA

g

+v-

i, q

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Physics of a Capacitor

Current:

Capacitance:

Note PassiveSign Convention:

C

i, q +v-

dq d Av A dvidt dt g g dt

A

Cg

dvi C

dt

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Energy in a Capacitor

Stored Energy:

C

i +v-

dvp vi Cv

dt pdt dw Cvdv

21

2W Cvdv Cv

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Inductors in SeriesL1 L2

+ v1 - + v2 -+ v -

i

1 2 1 2

di div v v L L

dt dt

1 2 eq

di div L L L

dt dt

1 2eqL L L

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Capacitors in Parallel

C1 C2

i1 i2

i

+v-

1 2 1 2

dv dvi i i C C

dt dt

1 2 eq

dv dvi C C C

dt dt 1 2eqC C C

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Inductors in Parallel

L1 L2

i

i1 i2+-

1 21 2 eq

i i iL L L

1 2

1 1 1

eqL L L

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Capacitors in Series

C1 C2

+ v1 - + v2 -

q q q

+ v -

1 21 2 eq

q q qv v v

C C C

1 2

1 1 1

eqC C C

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

RLC Circuit as a System

Kirchoff’s Voltage Law (KVL):

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

INPUT

SYSTEM

OUTPUT

RC Circuit as an Example of First order Linear Time Invariant System

from http://www.electronics-tutorials.ws/rc/rc_1.html with modifications

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

SYSTEM

INPUT

OUTPUT

INPUT

RC Circuit as an Example of First order Linear Time Invariant System from http://www.electronics-tutorials.ws/rc/rc_3.html with modifications

OUTPUT

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

SYSTEM

INPUT

OUTPUT

INPUT

RC Circuit as an Example of First order Linear Time Invariant System from http://www.electronics-tutorials.ws/rc/rc_3.html with modifications

OUTPUT

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

SYSTEM

INPUT

OUTPUT

INPUT

RC Circuit as an Example of First order Linear Time Invariant System from http://www.electronics-tutorials.ws/rc/rc_3.html with modifications

OUTPUT

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Integrator and Low Pass Filter from http://www.electronics-tutorials.ws/rc/rc_3.html

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Differentiator and High Pass Filter from http://www.electronics-tutorials.ws/rc/rc_3.html

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Lab 9 Circuits

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015

Next Time: MSP 430, Bring Computer and Install Code Composer

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